Influence of trapping potentials on the phase diagram of bosonic atoms in optical lattices

TL;DR

This paper investigates how external trapping potentials influence the phase diagram of bosonic atoms in optical lattices, revealing modifications to superfluid transitions and energy level populations.

Contribution

It introduces a generalized Bose-Hubbard model incorporating trapping potential structures, extending the standard framework to account for populated energy levels.

Findings

Trapping potentials significantly alter the superfluid transition properties.

Energy levels of the trap are populated at finite and zero temperature.

Comparison shows deviations from standard Bose-Hubbard predictions.

Abstract

We study the effect of external trapping potentials on the phase diagram of bosonic atoms in optical lattices. We introduce a generalized Bose-Hubbard Hamiltonian that includes the structure of the energy levels of the trapping potential, and show that these levels are in general populated both at finite and zero temperature. We characterize the properties of the superfluid transition for this situation and compare them with those of the standard Bose-Hubbard description. We briefly discuss similar behaviors for fermionic systems.